1. Field of the Invention
The present invention relates generally to Brillouin Fiber Optic Gyroscopes and more particularly, to an apparatus and method of decreasing the pump power requirement of a Brillouin Fiber Optic Gyroscope.
2. Description of the Prior Art
It is generally desirable to be able to decrease the input power requirement of any given system without affecting other system performance. Such a feature is especially desirable in a Brillouin Fiber Optic Gyroscope (BFOG), due to the large expense involved in supplying pump power, even in the milliwatt range.
At typical resonator cavity lengths of less than 100 meters, resulting in negligible fiber attenuation loss, the required pump power of a BFOG is inversely proportional to the length of the resonator coil. Under these conditions, it is feasible to reduce the input pump power by increasing the resonator coil length. However, other crucial system parameters are also dependent on resonator coil length, and a change in the resonator coil length will correspondingly impact other system performance. The most important of these resonator coil-length-dependent parameters are the dynamic range of gyroscope rotation rate, the resolution of the rotation rate measurement, the relative lock-in range, and the relative Kerr-effect-induced beat-frequency bias.
As described and claimed in U.S. Pat. No. 4,530,097, entitled "Brillouin Ring Laser," assigned to the assignee of the present invention, a BFOG comprises a laser source which provides pump light into a fiber. A directional coupler splits the pump light into two portions. The two portions are coupled into a resonator with one traveling in the clockwise (CW) direction and the other in the counterclockwise (CCW) direction in the resonator. The length of the resonator is adjusted so that the pump frequency matches one of the longitudinal modes in the resonator. When the pump power exceeds the threshold level for Brillouin oscillation, Brillouin waves will start propagating, resulting in bi-directional laser oscillations.
When the resonant cavity loop is at rest, both Brillouin waves will have the same resonant frequency. Upon rotation of the loop, each of the counterpropagating Brillouin waves will have a different optical path length around the loop due to the Sagnac effect because the optical path length for one of the waves increases, while the optical path length for the other wave decreases.
For instance, when the loop is rotated in a CW direction, the CW-traveling Brillouin wave will have a longer optical path around the loop than the CCW-traveling Brillouin wave. This difference in optical path length causes the resonant frequency for each wave to downshift or upshift accordingly, resulting in a frequency difference between the CCW and CW Brillouin waves. When the counterpropagating Brillouin waves are combined at the output, a beat-frequency is obtained. This beat-frequency is proportional to the rotation rate.
In a typical BFOG, the length of the resonator is adjusted through an asymmetrical feedback system so that one of the cavity resonant modes, for example, the CW cavity resonant mode, coincides with the pump frequency. When the gyro is not rotating, the CCW pump light is also resonant because the CCW and CW cavity resonant modes coincide with each other. However, once the gyro rotates, the CCW and CW cavity resonant modes split and the CCW pump light is no longer at the resonant peak center. This results in a lower CCW pump intensity and accordingly, a lower CW Brillouin intensity.
This phenomenon, known as the "resonant walk-off effect," restricts the dynamic range of gyroscope rotation rate of the gyro. The pump waves in a BFOG can resonate in the cavity only if the pump frequency falls within the resonance frequency peak. Therefore, the width of this resonance peak, .DELTA.f.sub.c, will directly affect the dynamic range of gyroscope rotation rate of the gyro. As the rotation rate of the gyro increases, the CCW pump intensity continues to decrease and eventually becomes too low to sustain a CW Brillouin wave. When this happens, the beat signal disappears, and the rotation rate cannot be measured. This phenomenon sets the limit for the maximum rotation rate of the gyroscope, that is, the dynamic range of the gyroscope rotation rate is limited.
There are multiple thresholds for different orders of Brillouin lasing in a BFOG. When the pump intensity reaches the first threshold for Brillouin stimulated scattering, the circulating pump power within the resonant cavity is pinned. Any additional pump input power above this pinned level is built up as the first-order Brillouin circulating power.
When the first circulating Brillouin power reaches the same level as the circulating pump power, the second-order Brillouin circulating wave is generated. The operating window between the first-order Brillouin threshold and the second-order Brillouin threshold is referred to as the first operating window of the BFOG.
If the gyroscope is operating at the maximum limit of the first window (i.e., the input pump power is just below the second-order Brillouin threshold), the maximum allowed separation of resonator mode frequencies seen by the CW and CCW pump waves is .+-.[(.sqroot.3)(.DELTA.f.sub.c /2)], where .DELTA.f.sub.c is the full width of the pump resonance peak at half maximum. This occurs where the CW pump is stabilized at the resonant peak center and the corresponding CCW pump is operating at the minimum intensity needed to sustain the generation of a Brillouin wave, which is one-quarter of the CW pump intensity. Therefore, the dynamic range of the gyroscope rotation rate or the maximum rotation rate of the BFOG .OMEGA..sub.MAX, corresponding to the maximum allowed frequency separation of the Cw and the CCW resonant modes is: ##EQU1## where S is the scale factor of the BFOG. The scale factor is the Brillouin beat-frequency obtained under unit rotation rate. It is expressed by the formula: ##EQU2## where A is the total effective sensing area of the gyro, L is the total cavity length, n is the refractive index of the fiber, and .lambda. is the wavelength of the light.
Since A is proportional to L, S is independent of L. However, .DELTA.f.sub.c is inversely proportional to L. Thus, an increase in L in the conventional manner will result in a corresponding decrease in the maximum rotation rate (i.e., the dynamic range of the rotation rate) of the gyroscope.
Accordingly, one of the goals of the present invention is to increase the coil length without reducing the maximum rotation rate (i.e., the dynamic range of the rotation rate) of the gyroscope.
The second system parameter affected by an increase in resonator coil length is the resolution of the gyroscope rotation rate measurement. The resolution of the gyroscope rotation rate measurement is limited by the linewidth of the Brillouin beat signal at the gyroscope output, and the latter is determined by the linewidth of the individual Brillouin lasing waves. A lasing wave has a particular linewidth, and this is the result of spontaneous emission noise which introduces incoherent energy to the oscillation mode. The linewidth of the lasing wave is much narrower than the cold cavity resonance linewidth, and its theoretical limit can be expressed by the Schawlow-Townes formula: ##EQU3## where h is Planck's constant, .nu. is the light frequency and P.sub.s,out is the Brillouin laser output power.
The resolution of the rotation rate measurement of the BFOG is governed by the formula: ##EQU4## where .DELTA.f.sub.ST is the Schawlow-Townes linewidth and S is the scale factor. At typical resonator cavity lengths of less than 100 meters, fiber attenuation loss is negligible. Under these conditions, .DELTA.f.sub.ST is inversely proportional to L. Thus, an increase in L in the conventional manner will imply a decrease in .delta..OMEGA.. This is a desirable factor in any BFOG system.
Accordingly, a second goal of the present invention is to reduce the input pump power of a BFOG while either increasing the resolution of the rotation rate measurement (i.e., reducing .delta..OMEGA.), or keeping it invariant, as a trade-off for keeping the dynamic range of the BFOG rotation rate invariant.
The third system parameter affected by an increase in resonator coil length is the lock-in range of the gyro. Optical coupling between the counterpropagating waves tends to pull the frequencies of these two Brillouin waves together. When the frequency difference of the counter propagating lasing waves decreases to a point, typically less than 500 Hz, the two Brillouin waves are locked into one frequency. This limits the minimum of the rotation rate of the gyro.
Since the absolute frequency lock-in range is inversely proportional to L, increasing L will result in a decrease in the lock-in range. Although this is also desirable, the absolute frequency lock-in range does not provide any meaningful determination of gyro performance. To be able to make that determination, the absolute lock-in range should be scaled to provide the ratio of the lock-in range to the total operational range. As previously discussed, the scaling factor is independent of L, and thus, an increase in L in the conventional manner will reduce the relative lock-in range, which is desirable in a BFOG system.
Thus, a third goal in the present invention is to decrease input pump power while either reducing the relative lock-in range of the BFOG system, or leaving the relative lock-in range invariant, as a trade-off for keeping the dynamic range of the BFOG rotation rate invariant.
The final system parameter of significance is the Kerr-effect-induced beat-frequency bias. The "resonant walk-off-effect" described above causes the two Brillouin waves in the cavity to have different circulating power levels when the gyro is rotating. This results in a beat-frequency bias through a phenomenon known as the "Kerr-effect." Basically, as the Brillouin waves travel through the optical fiber, the refractive index seen by a Brillouin signal is slightly modified by the signal's own intensity, as well as by other light intensities circulating inside the resonator. When the circulating intensities of the CW and CCW Brillouin signals are different or not balanced, the imbalance causes an effective difference in the optical path lengths of the cavity seen by these two waves. This imbalance of the Brillouin intensities and the resultant optical path length imbalance translates to a beat-frequency offset, sometimes known as the Kerr-bias which appears as a non-zero rotation rate even though the BFOG may not be rotating. This results in a spurious reading for the rotation rate measurement.
Since the Kerr-bias is proportional to the differential circulating power between the two Brillouin waves, it is proportional to the absolute Brillouin circulating power in the first window, P.sub.S,cir. As P.sub.S,cir is inversely proportional to L, assuming negligible fiber attenuation loss, it follows that the absolute Kerr-bias is reduced with an increase in L.
Again, the determination of gyro performance is described by the relative Kerr bias instead of the absolute Kerr bias. Thus, a determination of the Kerr-bias is again obtained through scaling. As discussed above, the scale factor is independent of L, so that increasing L in the conventional manner will lead to a decrease in the Kerr-bias. Thus, a fourth goal in the present invention is to reduce input pump power while either reducing the relative Kerr-effect-induced beat-frequency bias, or keeping it invariant, as a trade-off for keeping the dynamic range of the BFOG invariant.
Accordingly, there is a need in the art for a technique of reducing pump power requirement in a BFOG that does not degrade other system performance, particularly the important system parameters of: the dynamic range of the gyroscope rotation rate, the resolution of BFOG rotation rate measurement, the relative lock-in range and the relative Kerr-effect-induced beat-frequency bias.